Music and numbers

If we
explore the way the numbers in the sound ratios manifest itself, we may better
understand the old saying about numbers and music.

A historic known example is
Plato’s mathematical calculation of the Pythagorean scale. Plato did by inserting the
harmonic and arithmetic means respectively between each of the terms in the two
geometric progressions, 1,2,4,8 and 1,3,9,27 succeeded in corroborating
mathematically everything that Pythagoras had discovered on the strings of his
monochord or lyre. More about numbers and the Pythagorean Scale later.

First
we have to remember some basic about prime numbers, which first are: 2, 3, 5, 7,
11, 13, 17, 19, 23, 29….p. (Usually 1 is not considered a prime).

The
only even prime number is 2.

Prime
numbers are the building factor in the body of Natural numbers because any
number can be divided into primes in one and only one way. They are a product of
prime numbers.

Any
musical sound can be expressed into numbers by its ratio; e.g. 4:3, the Fourth,
which is the double of the double (2x2) and is effectively a repletion of the
fundamental and in that respect do not contain a new identity.

The
fifth harmonic on the other hand, the major third by the ratio of 5:4, is in
that respect a “new” interval with the prime number 5.

(The
musical terminology can be very confusing. The fifth harmonic is the major Third
referring to the third tone in the diatonic scale and so do the Fifth, which is
the third harmonic!

)

The
seventh harmonic got it right since it is called the Seventh and is considered
as another “new” identity.

Looking
at the 9th harmonic, the major second, 9:8, we have some more
confusion, since it should just be the third double above the fundamental, the
first odd composite, but because 9 is not the double of anything, it sounds like
something new.

The
purpose in saying that numbers and music has something more in common than
frequencies ratios, we have to
expand the scope into the symbolic representation of
numbers.

It may sound odd for the present man that musical scales reflects meta
physical properties. Nerveless, the ancient Eastern scales and the antique Greek
scales was deeply related to symbolic values of numbers.
Music was considered as a symbolic representation of the relationship between
heaven and earth and as such have to reflect the celestial influence. The
Pythagoreans believed that it was not necessary to go beyond the third power
(Cube) of a number, as one can not go above the three dimensions.

The Chinese
regarded the first 5 primary sounds of the fifths, the Pentatonic scale, as a
representation of the perceptible world (the five Elements), and the first 12
fifths (the circle of fifths) as an reflection of the Zodiac signs.
For the modal Indian music with
its 22 intervals with the 7 notes of the scale, a more subtle representation can
be found by regarding twenty two relating to seven in the ratio 22/7, which is the
approximate expression of the relation between the circle and its diameter, so
these two numbers represent the circle, the most perfect shape.